Locating Peaks and Valleys with Derivatives (Explaining Calculus #9)

We have gone through a couple of discussions now on how to actually calculate the value of a derivative. This is great, after all what good is a shiny new tool if you don’t know how to operate it? But we are done with that now. Now that we’ve gone through a tutorial with derivatives,Continue reading “Locating Peaks and Valleys with Derivatives (Explaining Calculus #9)”

Computing Derivatives: Part 2 (Explaining Calculus #8)

Most recently in the series on calculus, we did some overview on some “precalculus” topics that we’d need for later calculus discussions. Having now done this, we move on to several examples of more ‘complicated’ rules that derivatives follow. We will then investigate some more difficult specific functions and their derivatives. Finally, at the end,Continue reading “Computing Derivatives: Part 2 (Explaining Calculus #8)”

Topics From “Precalculus”: Part 2 (Explaining Calculus #7)

Because of the directions I’d like to be able to go later on in this series, we need to make an aside about more topics that aren’t specifically calculus related. If you’ve made it this far, great for you! You’re now getting into the realm of calculus. This is a fun ride, and it isContinue reading “Topics From “Precalculus”: Part 2 (Explaining Calculus #7)”

Computing Derivatives: Part 1 (Explaining Calculus #6)

In the previous post in this series, we set up a definition of the derivative of a function, which is a new function that tells us how the original function changes over time. Now that we have set up this idea of derivatives, we are going to enter into a period of showing how toContinue reading “Computing Derivatives: Part 1 (Explaining Calculus #6)”

Derivatives, Tangent Lines, and Change (Explaining Calculus #5)

We’ve spent a few posts now developing the ideas of limits and continuity, two of the foundational ideas of calculus. We are now going to introduce the third foundational idea, the derivative. The derivative can be thought of as a way to capture the way that things change over time into one single formula. InContinue reading “Derivatives, Tangent Lines, and Change (Explaining Calculus #5)”

Understanding Continuity (Explaining Calculus #4)

In both life and academic science, we often come across things that change incrementally over time. If we are buying a fast car, we want to know how quickly that car accelerates from 0 to 60 miles per hour – and the answer is most certainly not zero seconds – we first have to hitContinue reading “Understanding Continuity (Explaining Calculus #4)”

Working With Limits (Explaining Calculus #3)

In a previous post, I spent time talking about what limits are on a conceptual level, and some details about how they work on a practical level. Now, I want to run through a few examples to show how computing limits actually works, and in particular a very special kind of situation – which youContinue reading “Working With Limits (Explaining Calculus #3)”

What Is a Limit? (Explaining Calculus #2)

Sometimes, it doesn’t matter as much where things are right now, but where they are going. For example, I am writing this roughly six months into the COVID-19 quarantine in the United States, with the 2020 presidential election on the horizon. With an election nearing, there are a lot of polls out there about whoContinue reading “What Is a Limit? (Explaining Calculus #2)”

Topics from “Pre-Calculus” (Explaining Calculus #1)

Before we can go into a discussion of calculus itself, it is important to set up some of the underlying concepts that calculus uses. You might view this as something analogous to learning the letters of the alphabet before you can start learning to read words and sentences. Without letters, you aren’t going to beContinue reading “Topics from “Pre-Calculus” (Explaining Calculus #1)”

Explaining Calculus (Intro)

In our day and age, this word strikes fear into many hearts. Much like ‘rocket science,’ it is used in our culture to represent anything that is extremely difficult or even something incomprehensible. I am talking about calculus. Those who have taken a course in this topic will have a good idea of what kindsContinue reading “Explaining Calculus (Intro)”